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Unlabelled Gibbs partitions

Part of: Combinatorial probability Combinatorics Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  04 November 2019

Benedikt Stufler
Benedikt Stufler*
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland
*
Email: benedikt.stufler@math.uzh.ch
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Abstract

We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of weighted combinatorial objects. We describe a general setting characterized by the formation of a giant component. The collection of small fragments is shown to converge in total variation toward a limit object following a Pólya–Boltzmann distribution.

MSC classification

Primary: 60C05: Combinatorial probability 05A18: Partitions of sets
Secondary: 60B10: Convergence of probability measures
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 2 , March 2020 , pp. 293 - 309
Copyright
© Cambridge University Press 2019

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